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My impression based on experience (so somebody else might want to agree disagree): そのご is the more formal/written Japanese than そのあと which is more likely to be used in conversation/relaxed (if still neutral) circumstances. I've not heard そののち before but looking at spaceALC it seems to used mainly in novels (which would be why I don't know it) but possibly its appropriate to a more literary style?
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TimSep 3 '12 at 5:21

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I don't think I've ever seen そののち – but I have seen のち in things like 雨のち晴れ...
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Zhen LinSep 3 '12 at 8:58

そののち is often the reading in the Bible. Great question though, I've often wondered this as well.
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istrasciSep 3 '12 at 15:12

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This is my personal impression, but I think that その後 read as そのあと or そののち means “shortly after that” or “then,” whereas その後 read as そのご means a longer period than that, corresponding more to “ever since then.” そののち sounds more formal than そのあと to me.

Just to add to this, そのご is common, but you cannot say このご because this has been replaced by 今後. From this, you can see the resemblance to this answer, そのご <-> 今後, そのあと <--> このあと.
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Jesse GoodSep 4 '12 at 21:38